Right ok, so lets try a different approach, by changing the install location of the Origin games. Instead of the games being installed into program files (which requires admin privileges - try changing the location to My documents > Origin Games).
You can change the location where games will be installed within the Origin Client. Just select Origin (top left corner) > Application Settings > Advanced (the last tab on the left hand side) and then click on the "Change..." button underneath Downloaded Games - Your games will be installed to the following location.
